trans inv subsystem

codes/quantum/properties/block/topological/topological_abelian.yml

@@ -45,15 +45,17 @@ relations:
   parents:
     - code_id: topological
   cousins:
-    - code_id: qudit_subsystem_stabilizer
-      detail: 'All Abelian bosonic topological orders can be realized as modular-qudit subsystem stabilizer codes by starting with an Abelian quantum double model (slightly different from that of Ref. \cite{arxiv:2112.11394}) along with a family of Abelian TQDs that generalize the double semion anyon theory and \hyperref[topic:gauging-out]{gauging out} certain bosonic anyons \cite{arxiv:2211.03798}.
-      The stabilizer generators of the new subsystem code may no longer be geometrically local.
-      Non-Abelian topological orders are purported not to be realizable with Pauli stabilizer codes \cite{arxiv:1605.03601}.'
     - code_id: hamiltonian
       detail: 'Subsystem stabilizer code Hamiltonians described by an Abelian anyon theory do not always realize the corresponding anyonic topological order in their ground-state subspace and may exhibit a rich phase diagram.
       For example, the Kitaev honeycomb Hamiltonian admits the anyon theories of the 16-fold way, i.e., all minimal modular extensions of the \(\mathbb{Z}_2^{(1)}\) Abelian non-chiral non-modular anyon theory \cite{arxiv:cond-mat/0506438}\cite[Footnote 25]{arXiv:2211.03798}.'
     - code_id: walker_wang
       detail: 'Any Abelian anyon theory \(A\) can be realized at one of the surfaces of a 3D Walker-Wang model whose underlying theory is an Abelian TQD containing \(A\) as a subtheory \cite{arxiv:1907.02075,arxiv:2202.05442}\cite[Appx. H]{arxiv:2211.03798}.'
+    - code_id: 3d_stabilizer
+      detail: 'Qubit 3D stabilizer codes are conjectured to admit either fracton phases or abelian topological phases that are equivalent to multiple copies of the 3D surface code and/or the 3D fermionic surface code \cite{arXiv:1908.08049}.'
+    - code_id: translationally_invariant_subsystem
+      detail: 'All 2D Abelian bosonic topological orders can be realized as modular-qudit lattice subsystem codes by starting with an Abelian quantum double model (slightly different from that of Ref. \cite{arxiv:2112.11394}) along with a family of Abelian TQDs that generalize the double semion anyon theory and \hyperref[topic:gauging-out]{gauging out} certain bosonic anyons \cite{arxiv:2211.03798}.
+      The stabilizer generators of the new subsystem code may no longer be geometrically local.
+      Non-Abelian topological orders are purported not to be realizable with Pauli stabilizer codes \cite{arxiv:1605.03601}.'
 
 
 # Begin Entry Meta Information

codes/quantum/properties/stabilizer/topological_stabilizer/2d_stabilizer.yml

@@ -9,7 +9,7 @@ code_id: 2d_stabilizer
 name: '2D topological stabilizer code'
 
 description: |
-  Translationally invariant stabilizer code in two spatial dimensions.
+  Lattice stabilizer code in two spatial dimensions.
 
   Any prime-qudit code can be converted to several copies of the prime-qudit 2D surface code along with some trivial codes \cite{arXiv:1812.11193}.
 

codes/quantum/properties/stabilizer/topological_stabilizer/3d_stabilizer.yml

@@ -9,18 +9,11 @@ code_id: 3d_stabilizer
 name: '3D topological stabilizer code'
 
 description: |
-  Translationally invariant stabilizer code in three spatial dimensions.
+  Lattice stabilizer code in three spatial dimensions.
+  Qubit codes are conjectured to admit either fracton phases or abelian topological phases that are equivalent to multiple copies of the 3D surface code and/or the 3D fermionic surface code \cite{arXiv:1908.08049}.
 
-  Three-dimensional qubit codes can be characterized by four
-  coarse classes \cite{arXiv:1908.08049}:
+# 1. \textit{Abelian topological phase}: Excitations are mobile in all 3 dimensions, as is typical in a topological code. Such codes are conjectured to be equivalent to a \(\mathbb{Z}_2\) gauge theory, i.e., multiple copies of the 3D surface code or the 3D fermionic surface code.
 
-  1. \textit{Abelian topological phase}: Excitations are mobile in all 3 dimensions, as is typical in a topological code. Such codes are conjectured to be equivalent to a \(\mathbb{Z}_2\) gauge theory, i.e., multiple copies of the 3D surface code or its variant where the charge excitation is a fermion.
-
-  2. \textit{Foliated type-I fracton phase}: Excitations are mobile in less than 3 dimensions, but codes can be grown by \textit{foliation}, i.e., stacking copies of the 2D surface code.
-
-  3. \textit{Fractal type-I fracton phase}: Excitations are mobile in less than 3 dimensions, and codes are not foliated.
-
-  4. \textit{Type-II fracton phase}: Excitations are not mobile in any dimension and there are no string operators.
 
 
 relations:

codes/quantum/properties/stabilizer/topological_stabilizer/fracton.yml

@@ -7,18 +7,30 @@ code_id: fracton
 # includes Galois and modular
 
 name: 'Fracton stabilizer code'
-#introduced: '\cite{arXiv:quant-ph/9705052}'
+introduced: '\cite{arXiv:1101.1962}'
 
-description: 'A 3D translationally invariant stabilizer code whose codewords make up the ground-state space of a Hamiltonian in a fracton phase.'
+description: |
+  A 3D translationally invariant stabilizer code whose codewords make up the ground-state space of a Hamiltonian in a fracton phase.
+  Unlike topological phases, whose excitations can move in any direction, fracton phases are characterized by excitations whose movement is restricted.
 
+  Fracton codes are further classified into three sub-types:
+  \begin{enumerate}[(1)]
+  \item \textit{Foliated type-I fracton phase}: Excitations are mobile in less than 3 dimensions, but codes can be grown by \textit{foliation}, i.e., stacking copies of the 2D surface code and applying a constant-depth circuit.
+  \item \textit{Fractal type-I fracton phase}: Excitations are mobile in less than 3 dimensions, and codes are not foliated.
+  \item \textit{Type-II fracton phase}: Excitations are not mobile in any dimension and there are no string operators.
+  \end{enumerate}
 
 relations:
   parents:
     - code_id: 3d_stabilizer
-      detail: '3D stabilizer codes can realize fracton orders. Conversely, fracton codes need not be translationally invariant, and can realize multiple phases on one lattice.'
   cousins:
     - code_id: topological
-      detail: 'Fracton phases can be understood as topological defect networks, meaning that they can be described in the language of topological quantum field theory with defects \cite{arXiv:2002.05166,arxiv:2112.14717}.'
+      detail: 'Unlike topological phases, whose excitations can move in any direction, fracton phases are characterized by excitations whose movement is restricted.
+      Fracton phases can be understood as topological defect networks, meaning that they can be described in the language of topological quantum field theory with defects \cite{arXiv:2002.05166,arxiv:2112.14717}.'
+    - code_id: surface
+      detail: 'Foliated type-I fracton phase codes can be grown by \textit{foliation}, i.e., stacking copies of the 2D surface code.'
+
+ # Conversely, fracton codes need not be translationally invariant, and can realize multiple phases on one lattice.
 
 
 # Begin Entry Meta Information

codes/quantum/properties/stabilizer/topological_stabilizer/translationally_invariant_stabilizer.yml

@@ -10,12 +10,15 @@ name: 'Lattice stabilizer code'
 introduced: '\cite{arXiv:1101.1962,arXiv:1204.1063,doi:10.7907/GCYW-ZE58}'
 # geometrically local would also cover hyperbolic, Euclidean overlaps with CSS
 
+alternative_names:
+   - 'Topological stabilizer code'
+# 1D is not very topological...
+
 description: |
   A geometrically local qubit, modular-qudit, or Galois-qudit stabilizer code with qudits organized on a lattice modeled by the additive group \(\mathbb{Z}^D\) for spatial dimension \(D\).
-  If the stabilizer group is generated by site-local Pauli operators and their translations, then the code is called \textit{translationally invariant stabilizer code}.
-  Boundary conditions have to be imposed on the lattice in order to obtain finite-dimensional codes.
+  On an infinite lattice, its stabilizer group is generated by few-site Pauli operators and their translations, in which case the code is called \textit{translationally invariant stabilizer code}.
+  Boundary conditions have to be imposed on the lattice in order to obtain finite-dimensional versions.
   Lattice defects and boundaries between different codes can also be introduced.
-  It is possible to formulate a thermodynamic limit for lattice codes, with the 1D lattice version reducing to quantum convolutional codes.
 
   Translationally-invariant prime-qudit (\(q=p\)) stabilizer codes with \(m\) qudits per unit cell have been classified in dimensions \(D\in\{1,2\}\) in the thermodynamic limit, up to equivalence under local constant-depth Clifford circuits.
   Any 1D (2D) code can be converted to several copies of the 1D repetition code (prime-qudit 2D surface code) along with some trivial codes \cite{arXiv:1607.01387} (\cite{arXiv:1812.11193}).

codes/quantum/properties/stabilizer/topological_stabilizer/translationally_invariant_subsystem.yml

@@ -0,0 +1,37 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: translationally_invariant_subsystem
+# includes both Galois and modular
+
+name: 'Lattice subsystem code'
+introduced: '\cite{arxiv:0908.4246}'
+# geometrically local would also cover hyperbolic, Euclidean overlaps with CSS
+
+alternative_names:
+   - 'Topological subsystem code'
+# 1D is not very topological...
+
+description: |
+  A geometrically local qubit, modular-qudit, or Galois-qudit subsystem stabilizer code with qudits organized on a lattice modeled by the additive group \(\mathbb{Z}^D\) for spatial dimension \(D\).
+  On an infinite lattice, its gauge and stabilizer groups are generated by few-site Pauli operators and their translations, in which case the code is called \textit{translationally invariant subsystem code}.
+  Boundary conditions have to be imposed on the lattice in order to obtain finite-dimensional versions, in which case the stabilizer group may no longer be generated by few-site Pauli operators.
+  Lattice defects and boundaries between different codes can also be introduced.
+
+
+relations:
+  parents:
+    - code_id: oecc
+  cousins:
+    - code_id: translationally_invariant_stabilizer
+      detail: 'Lattice subsystem codes reduce to lattice stabilizer codes when there are no gauge qudits. The former (latter) is required to admit few-site gauge-group (stabilizer-group) generators on a lattice with boundary conditions.'
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2024-01-30'

codes/quantum/qubits/stabilizer/fracton/checkerboard.yml

@@ -0,0 +1,37 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: checkerboard
+physical: qubits
+logical: qubits
+
+name: 'Checkerboard model code'
+introduced: '\cite{arXiv:1505.02576}'
+
+description: |
+  A foliated type-I fracton code defined on a cubic lattice that admits weight-eight  \(X\)- and \(Z\)-type stabilizer generators on cubes of the lattice.
+  Variants include the twisted checkerboard model \cite{arxiv:1805.06899}.
+
+features:
+  decoders:
+    - 'Parallelized matching decoder \cite{arxiv:1901.08061}.'
+  code_capacity_threshold:
+    - 'Independent \(X,Z\) noise: \(\sim 7.5\%\), higher than 3D surface code and color code \cite{arXiv:2112.05122}.'
+
+
+relations:
+  parents:
+    - code_id: qubit_css
+    - code_id: fracton
+      detail: 'The checkerboard model is equivalent to two copies of the X-cube model via a local unitary \cite{arxiv:1806.08633}. Hence, it is a foliated type-I fracton code.'
+  cousins:
+    - code_id: xcube
+      detail: 'The checkerboard model is equivalent to two copies of the X-cube model via a local unitary \cite{arxiv:1806.08633}.'
+
+
+_meta:
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2024-01-30'

codes/quantum/qubits/stabilizer/topological/fracton/xcube.yml → codes/quantum/qubits/stabilizer/fracton/xcube.yml

@@ -11,7 +11,8 @@ name: 'X-cube model code'
 introduced: '\cite{arxiv:1603.04442}'
 
 description: |
-  A Type-I fracton code supporting a subextensive number of logical qubits.
+  A foliated type-I fracton code supporting a subextensive number of logical qubits.
+  Variants include the membrane-coupled \cite{arxiv:1701.00747} and twice-foliated \cite{arxiv:1806.08625} X-cube models.
 
 features:
   decoders:
@@ -22,8 +23,9 @@ features:
 
 relations:
   parents:
-    - code_id: qubit_stabilizer
+    - code_id: qubit_css
     - code_id: fracton
+      detail: 'The X-cube model is a foliated type-I fracton code \cite{arxiv:1803.10426,arxiv:1908.08049}.'
   cousins:
     - code_id: quantum_inspired
       detail: 'According to Ref. \cite{arxiv:2002.11738}, a classical analogue of the X-cube model is the eight-vertex model \cite{doi:10.1063/1.1665111,doi:10.1103/PhysRevLett.26.832,doi:10.1016/0003-4916(72)90335-1}.'

codes/quantum/qubits/subsystem/topological/color/doubled_color.yml

@@ -21,7 +21,8 @@ features:
 
 relations:
   parents:
-    - code_id: subsystem_color
+    - code_id: subsystem_css
+    - code_id: translationally_invariant_subsystem
   cousins:
     - code_id: divisible
       detail: 'Doubled color codes are constructed using a generalization of the doubling transformation \cite{arxiv:1012.4134} that combine doubly-even codes to make triply-even codes.'

codes/quantum/qubits/subsystem/topological/color/subsystem_color.yml

@@ -34,6 +34,7 @@ features:
 relations:
   parents:
     - code_id: subsystem_css
+    - code_id: translationally_invariant_subsystem
     - code_id: single_shot
       detail: 'The subsystem color code is a single-shot code \cite{arxiv:1503.08217}.'
   cousins:

codes/quantum/qubits/subsystem/topological/five_squares.yml

@@ -24,6 +24,7 @@ relations:
   parents:
     - code_id: subsystem_hypergraph
       detail: 'Generalized five-squares codes are special cases of subsystem hypergraph codes \cite[Sec. II.B]{arxiv:1805.12542}.'
+    - code_id: translationally_invariant_subsystem
   cousins:
     - code_id: surface
       detail: 'Decoding of five-squares codes leads to a mapping of these codes to two copies of the surface code \cite{arxiv:1012.0425,arxiv:1805.12542}.'

codes/quantum/qubits/subsystem/topological/heavy_hex.yml

@@ -48,6 +48,7 @@ realizations:
 relations:
   parents:
     - code_id: subsystem_css
+    - code_id: translationally_invariant_subsystem
   cousins:
     - code_id: surface
       detail: 'Surface code stabilizers are used to measure the Z-type stabilizers of the code.'

codes/quantum/qubits/subsystem/topological/subsystem_three_fermion.yml

@@ -20,6 +20,7 @@ description: |
 relations:
   parents:
     - code_id: subsystem_stabilizer
+    - code_id: translationally_invariant_subsystem
     - code_id: topological_abelian
       detail: 'The 3F code is a subsystme code characterized by 3F topological order \cite{arxiv:2211.03798}, which is chiral and modular.'
   cousins:

codes/quantum/qubits/subsystem/topological/surface/3d_subsystem_surface.yml

@@ -20,6 +20,7 @@ description: |
 relations:
   parents:
     - code_id: subsystem_css
+    - code_id: translationally_invariant_subsystem
     - code_id: single_shot
       detail: 'The 3D subsystem surface code is a single-shot code \cite{arxiv:2106.02621,arxiv:2305.06365}; see Ref. \cite{arxiv:2307.08118} for an alternative formulation.'
   cousins:

codes/quantum/qubits/subsystem/topological/surface/subsystem_rotated_surface.yml

@@ -19,6 +19,7 @@ description: |
 relations:
   parents:
     - code_id: subsystem_css
+    - code_id: translationally_invariant_subsystem
   cousins:
     - code_id: subsystem_surface
     - code_id: rotated_surface

codes/quantum/qubits/subsystem/topological/surface/subsystem_surface.yml

@@ -33,6 +33,7 @@ notes:
 relations:
   parents:
     - code_id: subsystem_css
+    - code_id: translationally_invariant_subsystem
   cousins:
     - code_id: surface
 

codes/quantum/qudits/subsystem/topological/qudit_znone.yml

@@ -19,6 +19,7 @@ description:
 relations:
   parents:
     - code_id: qudit_subsystem_stabilizer
+    - code_id: translationally_invariant_subsystem
     - code_id: topological_abelian
       detail: 'The \(\mathbb{Z}_q^{(1)}\) subsystem code is characterized by the \(\mathbb{Z}_q^{(1)}\) anyon theory \cite{doi:10.7907/5NDZ-W890}. The anyon theory has a single generator \(a \in \mathbb Z_N\) with \(\theta(a) =e^{\frac{2\pi i}{N}a^2}\). It is modular for odd prime \(q\) and non-modular otherwise.'
   cousins:

codes/quantum/qudits/subsystem/topological/semion.yml

@@ -21,6 +21,7 @@ features:
 relations:
   parents:
     - code_id: qudit_subsystem_stabilizer
+    - code_id: translationally_invariant_subsystem
     - code_id: topological_abelian
       detail: 'The semion code is a subsystem code characterized by the chiral semion topological phase.'
   cousins:

codes/quantum/qudits/subsystem/topological/zthree_znine.yml

@@ -18,6 +18,7 @@ description: |
 relations:
   parents:
     - code_id: qudit_subsystem_stabilizer
+    - code_id: translationally_invariant_subsystem
     - code_id: topological_abelian
       detail: 'The \(\mathbb{Z}_q^{(1)}\) subsystem code is characterized by a non-modular anyon theory with \(\mathbb{Z}_3\times\mathbb{Z}_9\) fusion rules.'
   cousins:

codes/quantum/qudits/topological/tqd_abelian.yml

@@ -17,10 +17,8 @@ description: |
 
 relations:
   parents:
-    - code_id: qudit_stabilizer
-      detail: 'All Abelian TQD codes can be realized as modular-qudit stabilizer codes by starting with an Abelian quantum double model along with a family of Abelian TQDs that generalize the double semion anyon theory and \hyperref[topic:code-switching]{condensing} certain bosonic anyons \cite{arxiv:2211.03798}.'
     - code_id: 2d_stabilizer
-      detail: 'All Abelian TQD codes can be realized as modular-qudit stabilizer codes by starting with an Abelian quantum double model along with a family of Abelian TQDs that generalize the double semion anyon theory and \hyperref[topic:code-switching]{condensing} certain bosonic anyons \cite{arxiv:2211.03798}.
+      detail: 'All Abelian TQD codes can be realized as modular-qudit lattice stabilizer codes by starting with an Abelian quantum double model along with a family of Abelian TQDs that generalize the double semion anyon theory and \hyperref[topic:code-switching]{condensing} certain bosonic anyons \cite{arxiv:2112.11394}.
       Abelian TQD codes need not be translationally invariant and can realize multiple topological phases on one lattice.'
     - code_id: topological_abelian
       detail: 'Abelian TQDs realize all modular gapped Abelian topological orders \cite{arxiv:2112.11394}.